...who had no( relation ) to the rest of the community except (that) of drawing dividends and occasionally attending a sharehold's meeting to dictate their orders to the management.
这里的 that 是指代上文出现的 relation ,是不可以省略的,这里,except that of = except the relation of .
说明：在英语句子中,为了避免前面某个名词的重复,往往用that（指代单数名词）和 those （指代复数名词）来指代,这种用法以 that 或 those 必须有后置定语为前提；
例如：1、The weather of Beijing is usually colder in winter than that of Shanghai（ that 指代 the weather ,of Shanghai 为后置定语）.
2、The bikes made in Shanghai are better than those made inTinjing.
后部分试翻译：他们除了抽取红利及偶尔参加业主会议向管理部门发布指令外,与社区已无其它关系.（请注意 “关系”）.